GAZA/JERUSALEM, July 19 (Reuters) - Israeli forces on Saturday pressed ahead with a ground offensive in the Gaza Strip, where Palestinian militants kept firing rockets deep into Israel's heartland, pushing the death toll past 300 in almost two weeks of conflict.

Palestinian officials said 65 Palestinians, at least 15 of them under the age of 18, have been killed since Israel sent ground forces on Thursday into the densely populated enclave of 1.8 million Palestinians.

During that time, more than 135 rockets have been fired from Gaza, though many were shot down by Israel's Iron Dome missile-defense shield, including some over the country's commercial capital Tel Aviv, causing no casualties.

The Israeli military said it killed 17 Palestinian gunmen while 21 others surrendered and were taken for questioning after the infantry and tank assault began in the territory dominated by the Islamist Hamas.

One Israeli soldier was killed in an apparent friendly fire incident, the military said, and several other troops were wounded in the ground operations. It said some 240 targets, including 21 concealed rocket launchers and 10 tunnels, have been attacked.

U.S. President Barack Obama said on Friday he had spoken to Prime Minister Benjamin Netanyahu, underscoring Washington's support for Israel to defend itself but raising concerns about "the risks of further escalation" and additional loss of innocent lives.

"We are hopeful that Israel will continue to approach this process in a way that minimises civilian casualties," Obama told reporters at the White House.

U.N. Secretary-General Ban Ki-moon planned to travel to the Middle East on Saturday in a bid to end the hostilities.

At an emergency session of the U.N. Security Council on Friday, U.N. political affairs chief Jeffrey Feltman condemned rocket fire into Israel but voiced alarm at "Israel's heavy response".

The Israeli land advance followed 10 days of barrages against Gaza from air and sea, about 1,500 rockets fired by Hamas into Israel, and failed attempts to secure a truce by Egypt, a broker of ceasefires in previous Israeli-Palestinian flare-ups.

"We chose to start this operation after we exhausted other options and reached the conclusion that without it we could pay a much higher price," Netanyahu said on Friday. "The main goal is to restore quiet.

"My instructions ... to the Israeli army, with the approval of the security cabinet, is to prepare for the possibility of a widening, a significant widening of the ground operation."

He did not say what form a broadened offensive might take. Israel says its forces have focused so far on seeking out tunnels Palestinian militants might use for cross-border raids and moving weaponry.

One such infiltration was thwarted on Thursday: the army said it had repelled 13 Hamas gunmen after they emerged from a tunnel close to an Israeli farming community.

Gaza officials said 299 Palestinians had been killed since fighting began on July 8 - most of them civilians, including at least 50 under the age of 18.

There have been two Israeli fatalities - the soldier and a civilian, who was killed by a rocket. More than 100 rocket bursts each day at southern Israel and the heartland Tel Aviv area have sent hundreds of thousands dashing for shelters.

INCURSION

Gaza residents said Israeli forces have moved several hundred metres (yards) into the north of the enclave and their deployment in the south of the territory was slightly deeper.

Hamas said its men were hitting Israeli tanks with mortar rounds and setting off bombs against troops crossing the sandy frontier under smokescreens.

Hospital officials said seven civilians were killed in an air strike overnight in southern Gaza. The Israeli military said it was looking into the report.

Hamas wants Israel and Egypt, whose military-backed government is at odds with the Palestinian Islamists, to lift border restrictions that have deepened Gaza's economic hardship and unemployment.

Israel briefly halted its Gaza assaults on Tuesday after accepting an Egyptian truce proposal. But Hamas, an offshoot of the outlawed Muslim Brotherhood in Egypt, said the plan failed to address its demands on ending the border blockades and releasing hundreds of its activists in the occupied West Bank held by Israel.

Though they are die-hard enemies, Israel says it does not intend to topple Hamas, the dominant Islamist force in Gaza.

The current conflict - the worst warfare between Israelis and Palestinians in two years - was stoked by the killing of three Israeli teenagers in the West Bank last month and the death on July 2 of a Palestinian youth in a suspected revenge murder.

Israel last mounted a large-scale invasion of the Gaza Strip during a three-week war in late 2008 and early 2009 that claimed 1,400 Palestinian and 13 Israeli lives. (Editing by Mohammad Zargham)

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